Average Error: 1.5 → 1.5
Time: 46.7s
Precision: 64
Internal Precision: 384
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[x + y \cdot \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original1.5
Target1.4
Herbie1.5
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.5

    \[x + y \cdot \frac{z - t}{z - a}\]
  2. Using strategy rm

  3. Applied div-sub1.5

    \[\leadsto x + y \cdot \color{blue}{\left(\frac{z}{z - a} - \frac{t}{z - a}\right)}\]
  4. Removed slow pow expressions.

Runtime

Time bar (total: 46.7s)Debug log

herbie shell --seed '#(1567391828 2030694642 2833800258 828025724 3004380912 3532991858)' +o setup:early-exit
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

  (+ x (* y (/ (- z t) (- z a)))))